It's 5 years I completed the Mechmate, and I always thought the right way to configure a Cnc router is to have the main long axe named X and the shorter named Y. This is what the plans say, this is what I have learned.
On some chinese machine I used, the Y axis is X and X is what we call Y .... isn't a crazy way don't you think ? (that's what I have thought).
Teaching the use of the machine to beginners I have payed a lot of attention to explain the orientation of the machine and the CAD design.
I operate the machine from the front, which I suppose is the same for you.
So looking the machine from the front, I have the Y axe that move from Left to Right or viceversa, and the X axe from closer to farther.
All of the CAD program work with the cartesian coordinate system where X increase fron left to right and Y from bottom to top.
If I design a rectangle on the CAD with the long side on the X axe, when I put the piece on the mechmate I always have to rotate it of 90 deg.
If in Mach3 I set up the Y-Car as X and The Gantry as Y I would get exacly the same orientation of the CAD. And Having setted the Zero in the closer left corner, any movement will be shown as positive in Mach3 coordinates.
I made many orientation mistakes in those years ... not easy for me to change now ... but I realy thinking on it (I have already made a second configuration with this setup and I also activated the homing and reference system).
What is your opinions guys ?

I stand on the side of my machine and X runs left to right and Y towards and away from me, same as I draw in Aspire.
For me it's WYSIWYG, and keyboard direction arrows for jog are intuitive. No rotating parts or thought processes here.

Normal ? what's normal ? :-)
Well, most of the Metal Milling Machine the X axis moves Left-Right ...
Me too I was taught ... But unless is normal to you to work the machine from the side, which is not for me as I load the material from the front, having the machine oriented the same way the cartesian coordinate system could avoid errors from design to loaded materials. ...... Just food for thoughts, I'm not teaching ... maybe just confused :-)
What I see is that for people learning from scratch is much easiear ....

I stand in front of the machine from where it is loaded, computer is on the left and have always set it how I draw so its Y for the longer axis (dual motors) so my 0,0 is near me and all movement is positive, for me this is most intuitive.
I see that almost every Chinese router is set this way so we must think alike

The 3D system allows for Right and left handed coordinates- the X and Y axis reverse places and the quadrant that has only positive values switch. In CNC machines the axis the tool is on is Z, and the long bed axis is X, the remaining is Y... a 0,0,0 position that originates in the bottom left corner can have positive x,y values in a right handed coordinate system, but a 0,0,0 that originates in the bottom right corner can also have positive x,y value if it is a left handed system.
The reason this always confuses me is the axis positive rotation rule - if you "hold" the axis in question with your thumb pointing in the positive direction your fingers will be pointing in the positive rotational direction... a conventional CNC spindle viewed through the spindle towards the work surface rotates clockwise.... and clockwise rotation with positve x,y values on the table only happen in a left handed cartisian grid quadrant that originates in the top left or bottom right corners assuming a long (x axis) in the horizontal orientation.

.. but Cartesian x,y coordinate values are dependent on Z axis rotation - the positive x values move right in a left handed ( clockwise ) system and move left in a right handed ( counterclockwise rotation ) system.... obviously the table is not going to transpose all those values because you reverse spindle direction to optimize a cut, but the values are also no longer true Cartesian either.

PS Al - I was also taught to think A=X ( A-cross) but it was to help remember the rotating axis of x is A... or ABC=XYZ works too!

assuming a horizontal x axis: the left handed system will generate positive x values moving LEFT and the right handed system will do it moving RIGHT - if y is pointing up and Z is pointing back towards you.... anyway

carry on.

x is the long work surface coordinate, y is the short one, and z moves up off the plane they create.

Just to clarify.
The rotation of a cutting tool has nothing to do with the coordinate system. You can use both right handed and left handed bits, and the coordinate system does not change.
This is different than a lathe spindle, or an A or B roary axis, which are actually spinning the workpiece.

Sergio...
I'm not sure there is a right or wrong way to layout the XY zero position on a CNC machine. That is, as long as it adheres to the Cartesian Plane and allow mathematics to work as is was designed some 400 years ago.

Placing the XY zero in any corner of the work surface simply requires use of negative / positive values of X & Y each of the 4 quadrants. The vast majority use the upper right quadrant with positive XY values away from zero.

That said, as a service tech for an OEM doing new installs of their product, many shops had other machines that operators had been trained on. These shops wanted the new machine reconfigured to match the existing. Of course I didn't see the logic in this and asked why the change made sense to them.

The responses were, of course varied, but had a familiar theme. That theme was that: "We/I learned it this way and it's the right way", and included some gems like:
The XY zero in the upper left corner, just like on a piece of paper
The Gantry Beam is always the X
The Gantry beam is always the Y
XY zero has to be in the Lower left corner (same for 3 other corners)
The X is always the long side
The Y is always the long side
The list goes on and on.

It does appear that each manufacturer uses the quadrant if their choice for their reasons. And instructs operators as tho its the only way. And, if you as an operator have 20 years on that machine, you believe it.

Just know that all XY corner placement is viable and this would be made evident by the XY zero datum selection when setting up a job in all design software packages. The only thing that would be "wrong" is using the above described "left hand" system that would make traditional math return erroneous results without a {-1} multiplyer on some calculations.

By the way the brand I did the most work for had a strong influence on Mechmate design. This design forces an operator to orient himself on what seems to be a side due to machine rails that extend above the table, and call that side "the front". Open sides of the machine are called ends.

"I'm just sayin" no right or wrong, just no left hand rules. And please, don't apply motor rotational direction to the Z. They are unrelated. Unless you apply the right hand rule of magnetic.......

It is easy to tell between which of us have or use machines, and me . All the more reason for me to get started on a kitchen table setup..
GC, do all design systems that allow the selection of 0,0,0 location also need the tables dimensions/steps info to define the size or ends of the x,y,z travel? and in the case of a system that originated in the top left corner ( bottom right Cartesian quadrant - positive x,negative y values ) would it display the negative Y values on the operator display or increasing positive numbers from the 0 point?

...no left hand, check. ... no rotation, check.
the only machine I have had experience on had a spindle that moved on a horizontal x,y and acted on a horizontal rotary axis parallel to x.
Thank you both!

John...
All of the control systems that I am familiar with have a method to enter a low and high "soft limit" for each axis. These usually work from table (absolute machine) coordinates so that no matter where a user places a local XY zero a file can be prerun for a "soft limit check".

Most also have limit switches on the low side of the XY. Some (mine for sure) have them on the high side of XY & Z.

Some have the ability to add "boundaries" that are similar to limits, but have a few different triggers and reaction to those "soft limit" hits.

Due to vises with the high Y side being fixed, I use the lower right quadrant on my CNC'ed Bridgeport Mill. There should be no issue with displaying correct coordinates on a DRO. That said, I have seen some instances where a user table configuration was a little more difficult to sync up with the viewer window. In any case the group here has a lot of knowledge, go for it!